Theory And Method Of Estimating Three-Dimensional Displacement With InSAR Based On The Modern Surveying Adjustment

Interferometric Synthetic Aperture Radar (InSAR), a space geodesy and modern remote sensing technique developed since1960s, can monitor the surface displacements with large scale, high precision, and continuous spatial coverage, which provides essential data for the investigation of the locomotory mechanism of the earth and the prevention of the natural and anthropogenetic geologic hazards, etc. However, the displacements acquired by conventional single-track InSAR can only reflect the projection of three-dimensional (3-D) displacements in Line-Of-Sight (LOS) direction, which may induce erroneous interpretation. This greatly hampers the development and application of InSAR. By combining the SAR data acquired from multi-track and multi-sensor, the one-dimensional measurements of InSAR can be extended to3-D. However, there is generally lacks of the rigorous theory of data processing in this field. In the integration of multi-sensor, multi-track and multi-temporal InSAR measurements, the existing methods do not fully consider the discrepancies of the temporal scales and geodesic precisions between these heterogeneous observations, and can not well handle the effects of InSAR multiple inherent errors. This greatly limits the accuracies and temporal resolutions of the derived3-D displacements.Modern surveying adjustment is a geodesy data processing technique based on the error theory and classical surveying adjustment, and has been developed in different aspects to form new theories and methods. Modern surveying adjustment has been widely used in the GPS, GIS and RS (3S) and its integrated data processing. Since the InSAR3-D displacements estimation is inherent an adjustment problem, the theories and methods of modern surveying adjustment are expected to be of great use in this field. The core research contents of the thesis are the function model, stochastic model and estimation criteria of the InSAR3-D displacements estimation. To circumvent the key difficulties in the InSAR3-D displacements estimation, the thesis studies the models and methods of modern surveying adjustment such as filtering, interpolation, least squares, variance component estimation, Kalman filtering, total least squares, etc, and thus presents a systematic research on the methodologies and models of exploiting InSAR measurements to derive3-D displacements based on the modern surveying adjustment. This provides a novel way for accurately estimating3-D surface displacements. The main contributions and innovations of the thesis are as follows:(1) The thesis constructs the function model of using InSAR to estimate3-D displacements based on the least squares (LS) adjustment, and designs the methods of InSAR ramp error correction for the observations of the function model. This greatly improves the accuracies of the InSAR3-D displacement estimations. The thesis analyses in depth the possibility and accuracy of using one-dimensional LOS measurement to estimate3-D surface displacements, and systematically studies the functional relationships between the heterogeneous InSAR (inclusing D-InSAR, Offset-Tracking and MAI) measurements and the3-D surface displacements. These are then extended into the function model of integrating heterogeneous InSAR and GPS measurements to estimate3-D displacements through theoretical derivation. In order to improve the accuracies of the azimuth displacement measurements by MAI, the thesis studies the spatial distributions of the ionospheric error and surface displacement, and develops an ionospheric ramp error correction method based on the directional filtering and interpolation. While for the discontinuity emerged between the D-InSAR measurements of adjacent tracks, the thesis exploits the connect points in the common area between the adjacent tracks as the additional constraint and thus develops a multi-track orbital ramp error correction method based on the Unified Simultaneous Least Squares (USLS) adjustment. On the basis of the developed function model and InSAR ramp error correction methods, the first3-D coseismic displacement fields of the2010Darfield, New Zealand earthquake and2011Tohoku-Oki, Japan earthquake have been mapped with an accuracy of cm level, respectively.(2) A novel InSAR3-D displacement velocity estimation model based on the variance component estimation (VCE) algorithm is proposed in the thesis. It conducts the posterior estimation of the stochastic model of the InSAR measurements. This greatly improves the accuracies of the InSAR3-D displacement velocity estimations. In order to estimate the optimal3-D displacement velocities from the LS adjustment, accurate stochastic model (i.e., variances) of InSAR measurements is also required. However, currently there is no well-developed method to estimate the accurate variances of the InSAR measurements. To slove this problem, the thesis divides the heterogeneous InSAR and GPS measurements into different groups according to their statistical natures, and then builds the function model between the LS residuals and the mean square error of unit weight of the heterogeneous InSAR and GPS measurements on the basis of the linear model. The posterior variances (or weights) of the heterogeneous InSAR and GPS measurements are finally estimated in an iterative procedure. Additionally, considering that abundant InSAR measurements cannot be acquired in practice, the thesis studies the optimal configuration of InSAR measurements in order to obtain the optimum blance between the accuracies of3-D displacement estimations and the burden of calculation. The novel method is validated with simulated data as well as real data acquired over Southern California, USA. The results show that the proposed method is superior to existing methods in terms of the accuracy. The novel method has also been applied to the Dongkemadi Glacier in Qinghai-Tibet Plateau. The first3-D movement velocity field of the alpine glacier is mapped. This provides a new perspective for the investigation of the ice mass transition and transformation of Qinghai-Tibet Plateau.(3) A novel InSAR3-D time series displacements estimation function model based on the Kalman filtering (KF) algorithm is proposed. It improves the temporal resolution and accuracies of InSAR3-D time series displacements. The conventional methods are limited by the temporal discrepancies between different sensors and different tracks SAR data, and can only resolve the3-D instantaneous displacements or3-D displacement velocities through the integration of the heterogeneous InSAR measurements. There is no method for InSAR 3-D time series displacement estimations. The thesis first analyzes in depth the limitation of using multi-sensor, multi-track and multi-temporal InSAR measurements to estimate3-D displacement evolutions, and then builds the observation and state functions for the3-D time series displacements estimation by exploiting the spatial-temporal correlations of the acquired InSAR measurements as constraints. They can be used to derive the dynamical estimations of3-D displacement. In order to improve the accuracies of the3-D time series displacement estimations, a variance inflation model is applied to suppress the gross errors such as unwrapping errors. In the real data processing, the3-D low-pass displacements and topographric residuals estimated by the InSAR time series analysising method based on LS are used to determine the filtering initials and to assist the InSAR phase unwrapping. This can further improve the estimating accuracy of the Kalman filtering. In the simulated and real data experiment carried out over Southern California, the novel method is proved that can estimate the3-D displacement evolutions for linear or nolinear ground movements in quasi-real-time, and reduce the computational burden and data storage. It also reveals that the novel method can obtain better3-D time series displacements in terms of temporal resolutions and accuracies than existing methods.(4) A novel InSAR3-D displacement estimation method based on the Total Least Squares (TLS) adjustment is proposed. It can fix the problem induced by the DEM error in conventional adjustment based on the Gauss-Markov (GM) model and thus improve the accuracies of the InSAR3-D displacement estimations. In the investigation of the surface-parallel ground displacements with InSAR, the DEM-derived slopes are needed to relax the requirement for multi-sensor and multi-track InSAR measurements. The error of the derived slope however will propagate into the coefficient matrix of the InSAR3-D displacement observation model. Conventional adjustment (e.g., LS) based on the GM model can only handle the errors in observations. Based on the Errors-In-Variables (EIV) model, the proposed method can minimize the summation of square errors of the observation errors and the coefficient matrix as well, and therefore can yield more accurate3-D displacement estimations. According to the commonly used configurations of InSAR measurements, the thesis designs two InSAR3-D models for surface-parallel displacements, one of which is based on the ascending and descending InSAR LOS measurements and the other based on the single-track InSAR LOS and azimuth measurements. The thesis then studies the propagation of the DEM errors (or the variances of slope angles) in the two models, respectively, and thus yields the variances of the coefficient matrix by theoretical derivation. The TLS estimations of the3-D surface displacements are then obtained. The results from the simulated and real data experiment carried out over Dasi Slope in Henan province, China show that the TLS adjustment is more robust in3-D displacement estimations than existing methods, and can improve the accuracies of the final results.